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On Fourier coefficient estimators consistent in the mean-square sense

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Popiński W.

Applicationes Mathematicae

1993-1995

tom 22

nr 2

275-284

The properties of two recursive estimators of the Fourier coefficients of a regression function $f \in L^2[a,b]$ with respect to a complete orthonormal system of bounded functions (e_k) , k=1,2,..., are considered in the case of the observation model $y_i = f(x_i) + η_i$, i=1,...,n , where $η_i$ are independent random variables with zero mean and finite variance, $x_i \in [a,b] \subset {\sym R}^1$, i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors $η_i$, i=1,...,n . Unbiasedness and mean-square consistency of the examined estimators are proved and their mean-square errors are compared.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Popiński W.

1 1994

Wyniki wyszukiwania

On Fourier coefficient estimators consistent in the mean-square sense